If you approximate a phase gradient state with stabilizers it kinda... just... works? Mostly? The approximation has a fidelity of ~80%, so there needs to be 80% overlap with the correct result even when doing things like QFTs that want fine grained angles. Weird!
https://algassert.com/quirk#circuit=%7B%22cols%22%3A%5B%5B1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22Z%5E%C2%BD%22%2C%22Z%22%5D%2C%5B%22Counting8%22%5D%2C%5B%22Chance8%22%5D%2C%5B%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%5D%2C%5B%22Swap%22%2C1%2C1%2C1%2C1%2C1%2C1%2C%22Swap%22%5D%2C%5B1%2C%22Swap%22%2C1%2C1%2C1%2C1%2C%22Swap%22%5D%2C%5B1%2C1%2C%22Swap%22%2C1%2C1%2C%22Swap%22%5D%2C%5B1%2C1%2C1%2C%22Swap%22%2C%22Swap%22%5D%2C%5B%22inputA2%22%5D%2C%5B%22H%22%5D%2C%5B%22inputA1%22%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22-%3DA2%22%5D%2C%5B1%2C%22H%22%5D%2C%5B%22inputA2%22%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22-%3DA3%22%5D%2C%5B1%2C1%2C%22H%22%5D%2C%5B%22inputA3%22%2C1%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22-%3DA4%22%5D%2C%5B1%2C1%2C1%2C%22H%22%5D%2C%5B%22inputA4%22%2C1%2C1%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C1%2C1%2C%22-%3DA5%22%5D%2C%5B1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22inputA5%22%2C1%2C1%2C1%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C%22-%3DA6%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22inputA6%22%2C1%2C1%2C1%2C1%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C%22-%3DA7%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22inputA7%22%2C1%2C1%2C1%2C1%2C1%2C1%2C%22%E2%80%A2%22%2C%22-%3DA8%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22Chance8%22%5D%2C%5B%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%5D%2C%5B%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%5D%2C%5B%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%5D%5D%7D
https://algassert.com/quirk#circuit=%7B%22cols%22%3A%5B%5B1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22Z%5E%C2%BD%22%2C%22Z%22%5D%2C%5B%22Counting8%22%5D%2C%5B%22Chance8%22%5D%2C%5B%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%2C%22%E2%80%A6%22%5D%2C%5B%22Swap%22%2C1%2C1%2C1%2C1%2C1%2C1%2C%22Swap%22%5D%2C%5B1%2C%22Swap%22%2C1%2C1%2C1%2C1%2C%22Swap%22%5D%2C%5B1%2C1%2C%22Swap%22%2C1%2C1%2C%22Swap%22%5D%2C%5B1%2C1%2C1%2C%22Swap%22%2C%22Swap%22%5D%2C%5B%22inputA2%22%5D%2C%5B%22H%22%5D%2C%5B%22inputA1%22%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22-%3DA2%22%5D%2C%5B1%2C%22H%22%5D%2C%5B%22inputA2%22%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22-%3DA3%22%5D%2C%5B1%2C1%2C%22H%22%5D%2C%5B%22inputA3%22%2C1%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22-%3DA4%22%5D%2C%5B1%2C1%2C1%2C%22H%22%5D%2C%5B%22inputA4%22%2C1%2C1%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C1%2C1%2C%22-%3DA5%22%5D%2C%5B1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22inputA5%22%2C1%2C1%2C1%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C1%2C1%2C%22-%3DA6%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22inputA6%22%2C1%2C1%2C1%2C1%2C1%2C%22%E2%80%A2%22%2C1%2C1%2C%22-%3DA7%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22inputA7%22%2C1%2C1%2C1%2C1%2C1%2C1%2C%22%E2%80%A2%22%2C%22-%3DA8%22%5D%2C%5B1%2C1%2C1%2C1%2C1%2C1%2C1%2C%22H%22%5D%2C%5B%22Chance8%22%5D%2C%5B%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%5D%2C%5B%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%2C%22Bloch%22%5D%2C%5B%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%2C%22H%22%5D%5D%7D
Comments